The climate and the landscape of Hungary are great for viniculture. There are 22 wine regions in the country, such as the great Tokaj, or Etyek. Every single one has their own characteristics, types and processes, so there's plenty to discover.
Your private host will know which regions are worth to visit, and they will be able to take you to the best wine cellars for wine tasting that is one of the obligatory things to do in Hungary. Make sure to have enough time for this awesome experience, and eat enough 'zsíroskenyér', a special Hungarian snack, between the fine glasses of wine.